Non-Consecutive Sudoku: rules and tips

Non-consecutive sudoku has one quiet extra rule: two cells that share an edge can never contain consecutive digits. A 5 can’t sit beside a 4 or a 6.

There are no marks on the grid at all, yet the rule is powerful enough that non-consecutive puzzles can be solved from remarkably few givens.

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The rules

Normal sudoku rules apply: 1 to 9 once in every row, column and 3×3 box.
Cells that share an edge never contain digits that differ by 1.
Diagonal neighbours are not restricted, and 9 and 1 are not consecutive.

How to start

Every digit casts a small shadow

When you place a digit, cross the two digits either side of it off its edge neighbours. Combined with ordinary scanning, this produces hidden singles everywhere.

Where is 4 in the top-left box? The 5 in its centre keeps 4 out of its four edge neighbours. The 4s in row 1 and column 1 rule out three corners, so the 4 goes in r3c3, diagonally next to the 5, which is allowed.

Middle digits are crowded

A 1 or 9 forbids only one digit from its neighbours; a 5 forbids two. Cells with many filled neighbours often have just one candidate left.

Rows of nine

Because consecutive digits can’t touch, every row and column is a little permutation puzzle: 4, 5 and 6 must all be separated from each other, for example. In a box, the centre cell touches four others, so it is the hardest place for a middling digit to live.

Common mistakes

Applying the rule to diagonal neighbours. Only cells sharing an edge are restricted.
Treating 9 and 1 as consecutive. They are not.
Forgetting that neighbours across a box border count too.

How the ranks scale difficulty

Every puzzle type on Hoot’s Puzzles comes in four ranks, named after the stages of a mathematical idea. Lemma is the warm-up: about a dozen more digits are given than logic strictly needs, and singles plus the variant’s own rule will carry you through. Proposition needs a real idea or two, typically pointing and claiming. Theorem is near-minimal, so almost every clue is load-bearing and you may need pairs. Conjecture gives the fewest digits and sparser rule clues: expect to think hard.

Non-consecutive puzzles have no extra clue marks, so rank is all about how many digits you start with and how deep the logic goes.

There are 99,999 puzzles per rank, each with its own number, so you can replay one or share it. Every type also has a 30-puzzle collection that climbs from Lemma to Conjecture. Every puzzle is checked to have exactly one solution that you can reach by logic alone, with no guessing.

Frequently asked questions

What is non-consecutive sudoku?

A sudoku variant in which no two cells sharing an edge may contain consecutive digits.

Does the non-consecutive rule apply diagonally?

No. Only cells that share an edge are affected.

Are 1 and 9 consecutive?

No. The digits don’t wrap around.